# cppicka: Picka's Reduced Window Estimator of Coverage Probability In lacunaritycovariance: Gliding Box Lacunarity and Other Metrics for 2D Random Closed Sets

 cppicka R Documentation

## Picka's Reduced Window Estimator of Coverage Probability

### Description

This function provides estimates of coverage probability from subsets of the observation window, which are a key component of balanced estimators of covariance, centred covariance, pair-correlation and gliding box lacunarity.

### Usage

```cppicka(xi, obswin = NULL, setcov_boundarythresh = NULL)
```

### Arguments

 `xi` An observation of a RACS of interest as a full binary map (as an `im` object) or as the foreground set (as an `owin` object). In the latter case the observation window, `obswin`, must be supplied. `obswin` If `xi` is an `owin` object then `obswin` is an `owin` object that specifies the observation window. `setcov_boundarythresh` To avoid instabilities caused by dividing by very small quantities, if the set covariance of the observation window is smaller than `setcov_boundarythresh`, then the returned pixel value is NA.

### Details

The plug-in moment covariance estimator (`plugincvc`) uses less of the observation window than the usual coverage probability estimators. Picka (1997, 2000) created new 'balanced' estimators of centred covariance and pair-correlation that accounted for this difference. A key component of Picka's estimators is an estimate of the coverage probability from the subregion of the binary map that is the intersection between W and W shifted by vector v, where W is the observation window (p.~687, Picka, 2000). If we treat X and W as indicator functions representing the foreground and observation window respectively, this coverage probability estimator used by Picka is

integral(X(u) W(u) W(u - v) du) / integral(W(u) W(u - v) du).

`cppicka` produces these estimates for an array of vectors v using fast Fourier transforms.

### Value

An `im` object. Pixel values correspond to estimates of the coverage probability from the subregion of the observation window, W, that is the intersection of W and W shifted by vector v, where v is the pixel location.

### Author(s)

Kassel Liam Hingee

### References

Picka, J.D. (1997) Variance-Reducing Modifications for Estimators of Dependence in Random Sets. Ph.D.: Illinois, USA: The University of Chicago.

Picka, J.D. (2000) Variance reducing modifications for estimators of standardized moments of random sets. Advances in Applied Probability, 32, 682-700.

### Examples

```xi <- heather\$coarse
obswindow <- Frame(heather\$coarse)
cp <- coverageprob(xi, obswindow)
cpp1 <- cppicka(xi, obswindow)
```

lacunaritycovariance documentation built on March 18, 2022, 5:20 p.m.